# Bayesian Multivariate Normal Model for Dissolution Profile Modeling This function implements the Bayesian multivariate normal model described in Pourmohamad et al (2022). ```r bmn(dis_data, B = 10000) ``` ## Arguments - `dis_data`: A data frame containing the dissolution data. The first column of the data frame should denote the group labels identifying whether a given dissolution belongs to the "reference" or "test" formulation group. For a given dissolution run, the remaining columns of the data frame contains the individual run's dissolution measurements sorted in time. Alternatively, the user may provide a data object of class dis_data containing the dissolution data. See the `make_dis_data()` function for the particular structure of the data object. - `B`: A positive integer specifying the number of posterior samples to draw. By default `B` is set to 10000. ## Returns The function returns a list of B posterior samples for the following parameters: * delta: A vector of posterior samples of delta as defined in Novick et. al 2015 * f2: A vector of posterior values of f2 * muR: A matrix of posterior samples for the reference group mean. Each row of the matrix corresponds to an observed time point, and each column of the matrix corresponds to a posterior sample. * muT: A matrix of posterior samples for the test group mean. Each row of the matrix corresponds to an observed time point, and each column of the matrix corresponds to a posterior sample. ## Note You should always check MCMC diagnostics on the posterior samples before drawing conclusions. ## Examples ```r ### dis_data comes loaded with the package ### We set B = 1000 to obtain 1000 posterior samples B <- 1000 post <- bmn(dis_data, B = B) ### We can check how well the posterior samples of the means are mixing by ### plotting the individual chains by time point burnin <- B * 0.1 # A 10% burn-in post$mu_R <- post$muR[,-(1:burnin)] post$mu_T <- post$muT[,-(1:burnin)] N <- B - burnin # Number of posterior samples after burn-in chains <- data.frame(samples = rep(c(1:N, 1:N), each = ncol(dis_data) - 1), group = rep(c("muR", "muT"), each = (ncol(dis_data) - 1) * N), timepoint = paste("Time Point", rep(1:(ncol(dis_data) - 1), 2 * N)), values = c(c(post$mu_R), c(post$mu_T))) g <- ggplot2::ggplot(chains, ggplot2::aes(samples, values)) + ggplot2::geom_line() + ggplot2::labs(x = "Iterations", y = "Posterior Sample Values") + ggplot2::facet_wrap(group ~ timepoint) + ggplot2::theme(text = ggplot2::element_text(size = 16)) ### If we want to calculate the Pr(f2 > 50) post$f2<- post$f2[-(1:burnin)] prob <- sum(post$f2 > 50) / (B - burnin) ### Or if we want calculate a 95% credible interval for f2 alpha <- 0.05 f2_cred <- c(quantile(post$f2, alpha / 2),quantile(post$f2, 1 - alpha / 2)) ``` ## References Novick, S., Shen, Y., Yang, H., Peterson, J., LeBlond, D., and Altan, S. (2015). Dissolution Curve Comparisons Through the F2 Parameter, a Bayesian Extension of the f2 Statistic. Journal of Biopharmaceutical Statistics, 25(2):351-371. Pourmohamad, T., Oliva Aviles, C.M., and Richardson, R. Gaussian Process Modeling for Dissolution Curve Comparisons. Journal of the Royal Statistical Society, Series C, 71(2):331-351.

bmn function